2.1 Returns and prices

To systematically vary expected return, time trend, and volatility of percentage return time series we create eight distinct return paths consisting of ten (hypothetical) annual returns each. Each return path consists of a deterministic trend (positive stable, negative stable, increasing, or decreasing) and a normally distributed noise term ${\epsilon }_t\sim N(\mu ,{\sigma }^2)$ with $\mu =0.0\%$ , ${\sigma }^2=1.4\%$ and $t=1,...10$ . Low-volatility assets consist of a linear return path plus the noise term for each year t. High-volatility assets have the same linear return paths but with the noise term multiplied by 6 before it is added.

Figure 1 shows each distinct return trend as a function of time, depicted as $RETURN$ charts (left) and $PRICE$ charts (right). Assets with a $POSITIVESTABLE$ trend are set up to yield positive returns fluctuating around a mean of 3% per year. The return path $INCREASING$ starts at − 3% in the first year and linearly increases to + 3% in the tenth year plus a noise term. Assets with trend negative stable contain the returns of the asset with trend positive stable multiplied by − 1. Analogously returns in trends decreasing are the returns of trend increasing multiplied by − 1. Price paths are generated by successively applying the corresponding returns to an initial price of 100.

Fig. 1

Return and price paths. This figure shows the four distinct return trends with the low volatility level as a function of time, depicted as return bar charts (left) and price line charts (right). For high-volatility assets, the added error term ${\epsilon }_t$ is multiplied by six

2.2 Experimental tasks

In the experiment subjects have to complete two main tasks, Task I and Task II. In both tasks participants were instructed to suppose that they want to invest 5000 euros. Subjects are then presented with charts of hypothetical assets and are asked to assess the respective riskiness and profitability of one asset at a time in Task I, and to compare two assets at a time along these dimensions in Task II. There are two variants for each task: either a return bar representation ( $RETURN$ ) or a line chart depicting the price development ( $PRICE$ ).

Task I consists of a 2 × 2 treatment design in which we vary the presentation format ( $RETURN$ or $PRICE$ ) and the presentation scale of the vertical axis ( $NARROW$ or $WIDE$ ) to identify these variables’ effect on risk perception as well as on return expectations and investment propensity. Subjects sequentially see eight different paths ( $RETURN$ or $PRICE$ ) and have to assess the assets’ riskiness and estimate its returns over the following year and over the next five years.Footnote ⁴ Whenever subjects are presented with return charts they are explicitly asked about future returns; when they see price charts they are asked to estimate future prices.Footnote ⁵ Each participant was presented with eight out of 16 possible return (price) charts (eight different assets in two different presentation formats, $NARROW$ and $WIDE$ ) in which each chart has the same probability of appearing. The order in which participants saw the assets was randomized and participants were not aware of being presented only with a selection of the possible assets.

In Task II subjects make pairwise comparisons between assets regarding their riskiness and expected return. In a 2 × 2 design the combinations of volatility and scale of the vertical axis are varied in four distinct conditions: same scale/same volatility, same scale/different volatility, different scale/same volatility, and different scale/different volatility. Except for Condition $SAME$ (same scale and same volatility), we name each condition after the variable in which the two charts of a pair differ. With this set-up we are able to generate a distinct number of 16 pairs for Condition $SAME$ ,Footnote ⁶ four pairs for Condition volatility, and eight pairs each for conditions scale and both. Subjects are presented with a total of eight randomly chosen pairs—two for each condition. In this task subjects have to compare two assets at a time. They are asked to decide which of the two assets they perceive as riskier; which asset they think is more profitable; and which asset they would rather invest in. For each question there is also the possibility to choose the neutral option ‘the same for both’ (later also referred to as ‘indifferent’).

In total, 32 charts have been considered: 4 trends × 2 volatilities (high/low) × 2 formats (return/price) × 2 scales (wide/narrow) = 32; 16 price charts and 16 return charts. For both tasks there are two variants: In Tasks Ia and IIa subjects are presented with return charts, in Tasks Ib and IIb they see price charts. In Task I, each subject considers eight random return charts (Ia) and eight random price charts (Ib), and in Task II each subject considers eight random return chart comparisons (IIa) and eight random price chart comparisons (IIb). Hence, each subject sees a potentially different selection of charts. The order is randomly determined and subjects are randomly assigned to one of two groups to eliminate any order effects (see Fig. 2 for the timeline and the two possible sequences).

In both presentation formats we vary the scale of the vertical axis to create a $NARROW$ and a $WIDE$ representation of each asset’s past performance. In return charts, the maximum value on the vertical axis and the tick size of $WIDE$ -scaled representations are three times the corresponding values of representations with scale $NARROW$ . For price charts the scales are adapted analogously. Figure 3 shows an example of $RETURN$ charts (top) and $PRICE$ charts (bottom), each with presentation scales $NARROW$ (left) and $WIDE$ (right). In each return (price) chart the value zero (100) as well as each tick (with precise values depending on asset and scale) is at exactly the same position in the graph to maintain consistency. Additionally, in order to reduce noise in estimating prices we provide the last price in the upper right corner of price charts (Glaser et al. Reference Glaser, Iliewa and Weber2018). In the instructions, we explicitly point out that the scale of the vertical axis might change over the course of the experiment. This note also appears when subjects review the on-screen instructions at any point in time during an experimental task. This prominently-placed reminder should ensure that our results are not driven by subjects’ inattention to the scale. To guarantee subjects’ understanding of the term ‘return’ we also include a definition stating that the return is defined as the percentage change of the price over one year. Table 1 summarizes the asset- and chart-specific variables and respective options: each chart is a distinct combination of volatility, trend, presentation format, and scale.

Fig. 2

Graphical overview of the experimental procedure. Subjects are randomly assigned into two groups with Group 1 being presented with $RETURN$ charts first (Tasks Ia and IIa) and $PRICE$ charts second (Tasks Ib and IIb) and Group 2 vice versa. Both groups complete a multiple price list task (MPL) and a certainty equivalence task (CET) to elicit risk and loss aversion parameters, as well as a questionnaire after the experiment

Table 1

Summary of variables in each performance chart

	Variable	Possible options
Asset specific	Volatility	$LOW$ or $HIGH$
	Trend	$POSITIVESTABLE$ ,
		$NEGATIVESTABLE$ ,
		$INCREASING$ ,
		or $DECREASING$
Chart specific	Presentation format	$RETURN$ or $PRICE$
	Scale (vertical axis)	$WIDE$ or $NARROW$

This table summarizes the relevant variables in specific to assets and charts: the volatility and trend of an asset, and the presentation format and scale of a chart

2.3 Implementation of the experiment

We conducted nine experimental sessions with a total of 193 students of business administration or economics in May and June 2017 at the Innsbruck EconLab at the University of Innsbruck. The experiment was programmed and conducted using oTree by Chen et al. (Reference Chen, Schonger and Wickens2016). Subjects were recruited with hroot by Bock et al. (Reference Bock, Baetge and Nicklisch2014). 45% of subjects were female; the mean age was 23; and about 51% of subjects had completed an undergraduate course in financial management.

In total, each session lasted approximately 40 min. This included studying on-screen instructions for each part of the experiment as well as a multiple price list task measuring subjects’ risk attitudes (Holt and Laury Reference Holt and Laury2002) and a certainty equivalence task to assess loss aversion (Gächter et al. Reference Gächter, Johnson and Hermann2010) using oTree applications by Holzmeister (Reference Holzmeister2017). After the main experiment subjects completed a questionnaire assessing their risk attitudes and demographics. A graphical overview of the experimental procedure, as well as the experimental instructions, screenshots of the decision tasks, and exemplary charts for each condition are provided in Online Appendices C, D, and E.

Subjects are incentivized by being paid one randomly chosen return of the asset they chose to rather invest in in one randomly chosen pair they were presented with for both parts (prices and returns) of Task II.Footnote ⁷ The chosen return times two is added to an initial amount of 5 euros for each task. For example, if the chosen asset of the randomly drawn pair pays 10% in the randomly drawn year, the participant receives 5 euros $\times (1+2\times 0.10)=6$ euros for this task. Total payouts varied between 6.30 euros and 16.30 euros with a mean of 11.65 euros; these include payouts from the risk and loss aversion tasks.

Fig. 3

Exemplary representations of the $LOW$ -volatility asset with trend $DECREASING$ in a $RETURN$ chart (top) and a $PRICE$ chart (bottom) for presentation scales $NARROW$ (left) and $WIDE$ (right). For return charts the value zero and for price charts the initial price of 100 as well as each tick are at the same positions for both scales. In return bar representations the tick size on a $WIDE$ scale is three times the one on a $NARROW$ scale; tick sizes in price representations are adjusted accordingly

3.1 Risk perception in individual assessments

We start our discussion by examining the influence of the scaling of the vertical axis on risk perception. We present analyses along the following dimensions: for both presentation formats ( $RETURN$ and $PRICE$ charts) we compare the influence of scaling of the vertical axis ( $WIDE$ vs. $NARROW$ ). To get a comprehensive picture we do this separately for the four different return trends ( $POSITIVESTABLE$ , $NEGATIVESTABLE$ , $INCREASING$ , and $DECREASING$ ), where we have each return trend once with a low and once with high level of return volatility ( $LOW$ or $HIGH$ ).

Figure 4 shows the differences in average perceived risk (elicited on a scale from 1 to 7) for each asset from $RETURN$ charts (left panel) and $PRICE$ charts (right panel). The differences are from the same asset being displayed once with a $WIDE$ and once with a $NARROW$ scale.Footnote ⁸ The four bars in each group of bars represent the four different trends; $LOW$ volatility is shown in the left group of each panel while $HIGH$ volatility is shown in the right group of each panel.

Fig. 4

Differences in average perceived risk (in NARROW minus WIDE) by trend and scale presented as $RETURN$ charts (left) and $PRICE$ charts (right). This figure depicts differences in average perceived risk (on a scale from 1 = “not risky at all” to 7 = “very risky”) for $RETURN$ chart and $PRICE$ chart representations of $LOW$ (left bars in each panel) and $HIGH$ (right bars in each panel) volatility assets. p-values above the bars are from Fisher-Pitman permutation tests on the subject-demeaned data. Each of the sixteen bars summarizes between 179 and 206 observations

Result 1 In individual assessments assets are perceived as riskier when presented on a $NARROW$ scale than when presented on a $WIDE$ scale.

Support For all assets, except those with a $POSITIVESTABLE$ trend, a $NARROW$ scale leads to higher perceived risk compared to a $WIDE$ scale. This holds for both presentation formats and both volatility levels. To test the statistical significance of the differences between charts with $NARROW$ and $WIDE$ axis scales, we run Fisher-Pitman permutation tests on the subject-demeaned data.Footnote ⁹ 10 out of 12 tests for assets other than with a $POSITIVESTABLE$ trend deliver p-values of 0.02 or smaller (the remaining two having p-values of 0.09 and 0.11, respectively), corroborating that assets are perceived riskier when presented on a $NARROW$ scale—we conjecture that this is the case because fluctuations are easier visible on a $NARROW$ scale. As the $POSITIVESTABLE$ trends show the lowest overall risk perceptions we conjecture that the non-difference in their perceived riskiness results from the fact that these always-positive returns (monotonically increasing prices, respectively) are never perceived as risky, no matter how they are displayed or whether they fluctuate more.

As we prominently make subjects aware of varying axis scales in the instructions, and as we find no relationship between the differences in risk perception and the time it took subjects to complete all related tasks,Footnote ¹⁰ we attribute the reported differences in perceived risk to the differences in axis scales, as the differences seem not to stem from subjects being unaware of the varying axes or inattentively clicking through the tasks.

Regarding different return paths we observe that the $POSITIVESTABLE$ trend is seen as least risky with average assessments between 2.08 and 3.51 on a 7-point scale, whereas $NEGATIVESTABLE$ and $DECREASING$ trends are viewed as carrying the highest risk (average riskiness assessments between 4.52 and 5.94) with trend $INCREASING$ being in-between across all presentation formats.Footnote ¹¹ This implies that an asset’s volatility (standard deviation of returns) does not necessarily determine people’s perceptions about its risk: e.g., for trend $NEGATIVESTABLE$ we find no difference in perceived risk between the $LOW$ - and $HIGH$ -volatility assets in return and price charts ( $p=0.17$ and $p=0.40$ )—even though their volatility differs by a factor of six. Furthermore, the standard deviation is the same for $NEGATIVESTABLE$ and $POSITIVESTABLE$ , but they are at opposite ends regarding perceived riskiness. This shows that subjects perceive losses (negative returns) as risk, while profits are perceived as not risky, even if they vary as much as losses do.Footnote ¹²

Additionally, one remarkable side result with potentially important implications for practitioners and regulators is that people perceive risk as significantly higher when presented with $RETURN$ charts as compared to $PRICE$ charts (five out of eight p-values are significant at $p<0.01$ ; all differences have the same sign; details are provided in Online Appendix B).

3.2 Expected returns in individual assessments

Besides eliciting subjects’ perceptions about risk we also asked participants to enter point estimates of future returns (when $RETURN$ charts were shown) or future prices (when $PRICE$ charts were shown) for a shorter (one year) and a longer (five year) horizon.Footnote ¹³ We discuss short-term forecasts first. The upper panels of Fig. 5 depict the median one-year-ahead return expectations for each asset (vertical axis) in relation to the last return (horizontal axis) in both presentation formats for scales $WIDE$ and $NARROW$ .

Fig. 5

Median one-year and five-year return forecasts. This figure shows the median one-year (upper panel) and five-year (lower panel) return forecasts as a function of the most recent return, i.e. the return in Year 10. For better visibility, i.e. to avoid overlapping medians, we add 0.15% to the most recent return of scaling $NARROW$ and deduct 0.15% for those of scaling $WIDE$ on the horizontal axis. Each point represents the median of between 83 and 109 observations

Result 2 Expected returns are driven by the latest return. We find no systematic influence of the scale on return expectations in individual assessments.

Support Short-term return forecasts are not the same across assets, but strongly depend on the last return. Subjects thus seem to behave as short-term trend-followers. With an $R^2$ of 0.97 and a slope of 0.76 the past return almost perfectly explains return predictions when returns are shown (upper-left panel of Fig. 5). When prices are shown (right panel) there is more dispersion, especially when the last return is negative. Still, with a slope of 0.98 and a $R^2$ of 0.85 the last return is a very good predictor of expected returns. This is consistent with Grosshans and Zeisberger (Reference Grosshans and Zeisberger2018), who analyze forecasts for price paths similar to the $INCREASING$ and $DECREASING$ trends in the present study, as they also report strong beliefs in short-term trend continuations. In both presentation formats we do not find a systematic influence of the scale ( $NARROW$ or $WIDE$ ).

We also asked subjects for their five-year return prediction (return per year); respectively price prediction (price in five years). For returns we find a very similar and consistent pattern to the one-year-predictions where the last return is again a very good predictor with a slope of 0.82 and an $R^2$ of 0.90 (see lower panels of Fig. 5). Returns calculated from $PRICE$ predictions also show a strong positive relation between last return and expected return. However, with a slope of 0.42 and an $R^2$ of 0.50 the relation is markedly flatter and weaker than for the one-year price data or the $RETURN$ data. In contrast to Glaser et al. (Reference Glaser, Langer, Reynders and Weber2007) we find that even for five-year-ahead forecasts, on average participants do not expect trend reversals to the extent of a change in signs—we find that the slope calculated from prices is only half as steep as for the one-year forecasts.

3.3 Investment preferences in individual assessments

We elicit subjects’ propensities to invest (on a scale from 1 to 7) for each of the displayed return and price charts. We find these to be negatively related to perceived riskiness,Footnote ¹⁴ i.e. assets with a $POSITIVESTABLE$ trend are the ones subjects would most like to invest in, while those with $NEGATIVESTABLE$ trends are least preferred. What we are interested in, however, is, whether there are differences in investment preferences between scales ( $NARROW$ vs. $WIDE$ ), i.e. whether the differences in risk perception we report in Section 3.1 translate into differences in investment propensities.

Result 3 Investment propensity is driven by an asset’s historical return and volatility as well as by subjective risk perception and expected returns. Varying the scale, however, has almost no influence on investment propensity.

Support Fig. 6 summarizes subjects’ answers by displaying the differences in average investment propensity (value in $NARROW$ minus value in $WIDE$ ) by trend and scale presented as $RETURN$ charts (left) and $PRICE$ charts (right). We only find a significant difference for $DECREASING$ trends in $PRICE$ charts, i.e. there is a higher likelihood to invest when these are displayed with a $WIDE$ scaling, while the other 14 tests do not yield significant differences. Hence, we do not find large, systematic differences between scales regarding subjects’ investment propensity.Footnote ¹⁵

Fig. 6

Differences in average investment propensity (in NARROW minus WIDE) by trend and scale presented as RETURN charts (left) and PRICE charts (right). This figure depicts differences in average investment propensity (on a scale from 1 = “very unlikely to invest” to 7 = “very likely to invest”) for $RETURN$ chart and $PRICE$ chart representations of $LOW$ (left bars in each panel) and $HIGH$ (right bars in each panel) volatility assets. p-values above the bars are from Fisher-Pitman permutation tests on the subject-demeaned data. Each of the sixteen bars summarizes between 179 and 206 observations

To explain investment behavior more comprehensively, we estimate least squares regressions similar to Nosić and Weber (Reference Nosić and Weber2010, also see Sarin and Weber Reference Sarin and Weber1993; Jia et al. Reference Jia, Dyer and Butler1999). The estimates suggest that besides an asset’s historical return and volatility, lower perceived risk of an asset (given a specific presentation format) and especially higher long-term expected returns increase the likelihood of investing, confirming the intuition that investment propensity substantially relies on people’s subjective assessments.Footnote ¹⁶

4.1 Risk perception in pairwise comparisons

Result 4 Different scaling can distort people’s perception about an asset’s risk in pairwise comparisons of assets with the same volatility, as assets shown on a $NARROW$ scale are perceived as more risky.

Support From the first row of panels in Fig. 7 we see that even when the two displayed assets have the same volatility and there is no difference in the scale, a surprisingly high share of between 24% and 60% of subjects perceive risk differently between the two assets. The share who perceives the risk differently is significantly higher for $INCREASING$ and $DECREASING$ trends than for $POSITIVESTABLE$ and $NEGATIVESTABLE$ trends ( $p<0.01$ ).Footnote ¹⁷ This holds for $RETURN$ as well as $PRICE$ charts. Probably subjects saw the similarity between the two charts/price paths shown, but thought there must be some difference to find and hence considered the two paths as differently risky. Data supporting this line of argumentation is the time subjects needed until they reached a decision: even though the scales are all equal (and thus easiest to compare) in Condition $SAME$ , subjects took significantly longer here (25.02 sec. on average) than in any other condition (between 21.74 and 23.35 sec.)

The second line of panels of Fig. 7 shows the distribution of choices for Condition $SCALE$ , i.e. when the asset volatility is the same but the scale is different ( $NARROW$ on one side, $WIDE$ on the other). One could argue that this is the ‘trap’ case where two identical assets are shown with different scaling to see whether subjects can be misled and thus perceive the asset shown with the narrower scale as more risky. This is indeed the case in 21% to 49% of all cases, while the asset with the wider scale is perceived as riskier in only 2% to 9% of all cases (in the remaining cases subjects are indifferent—most likely correctly seeing that only the scaling is different between both sides). Results are similar for $RETURN$ and $PRICE$ charts.

In ‘vertically’ comparing subjects’ risk assessments between conditions $SAME$ and $SCALE$ , where we vary the scale while keeping volatility constant, we find no significant difference in the proportion of ‘correct’ choices (in the sense of being indifferent between two almost identical or identical assets, i.e. with the same volatility): the average rates are 58% and 60%, respectively.

Result 5 Different scaling can distort people’s perception about an asset’s risk in pairwise comparisons of assets with different volatilities. Depicted with the same scale, subjects regard the more volatile asset as riskier; with differing scales, a considerable fraction erroneously perceives the less volatile asset as riskier or views them as equally risky.

Support In the third row of panels of Fig. 7 we present the case where the volatility of the two assets varies by a factor of six while the scale is the same (Condition $VOLATILITY$ ). Here, both assets are displayed on exactly the same axes and it should thus be comparatively easy to identify the more volatile asset and, if volatility is perceived as ’risk’, also to identify this asset as the riskier one. We find that with a $POSITIVESTABLE$ trend in $RETURN$ charts, almost 100% of subjects do exactly that. We also report very high shares of 90% and above identifying the more volatile asset as the riskier one for $DECREASING$ trends, both in $RETURN$ and $PRICE$ charts, and for $POSITIVESTABLE$ and $INCREASING$ trends in $PRICE$ charts. For $INCREASING$ trends in $RETURN$ charts we find 17% of subjects to be indifferent between the two assets—most likely as both trends start negative and then mostly increase, which is perceived as equally good, irrespective of volatility. An interesting case are the $NEGATIVESTABLE$ trends, especially for $RETURN$ (but also, to a lesser degree, for $PRICE$ ) charts: here around 20% do not see the less volatile asset as the less risky one. For $RETURN$ charts, 15% even consider the more volatile asset as less risky. We conjecture that this is the case as all returns in the low-volatility case are clearly negative—hence, an investor always loses with this asset. With high volatility, the dispersion of returns is much wider and thus the chance of earning a positive return is also higher. The corresponding asset is therefore perceived as less risky in about every sixth decision.

Finally, the fourth row of panels in Fig. 7 displays the choices in Condition $BOTH$ , where the shown assets differ in their volatility and additionally in their scaling. Note that in this condition, one side depicts a low-volatility asset and the other a high-volatility asset, hence different scales lead to both assets being displayed either on a $WIDE$ or on a $NARROW$ scale with the respective bars having comparable magnitudes. Comparing the results in this condition to the ones in the third row of panels we see that the choices are now more dispersed. While the high-volatility asset is still perceived as the more risky one in the majority of cases (between 56% and 85% of cases), ‘indifferent’ (up to 34%) and a preference for the low-volatility asset (up to 22% of cases) are chosen markedly more frequently than when the scaling is the same. In this cognitively demanding condition, results between and within $RETURN$ and $PRICE$ charts vary more than in other conditions. In particular, with trend $POSITIVESTABLE$ almost 20% see the low-volatility asset as the riskier one in return charts but choose ‘indifferent’ in price charts. We conjecture that in both cases subjects are misled by the different scalings. For trend $INCREASING$ , however, in a remarkably high share of 34% of decisions subjects are indifferent between the high- and low-volatility assets with $RETURN$ charts (for $PRICE$ charts the respective number is only 11%). We argue that for these subjects the main decision criterion is the clear upward trend in returns, while the details of the vertical axis scale and the exact values play a smaller role.

Assets with trend $NEGATIVESTABLE$ (third group of bars) are again a different story: a significantly higher share of subjects picks the less volatile asset as the riskier one than in any other trend bar $POSITIVESTABLE$ with $RETURN$ charts (all other $p<0.05$ ). This hints at losses being a driving force behind risk perception as all returns are negative in the low-volatility asset but not in the high-volatility one. Hence, in the $NEGATIVESTABLE$ trend, having more volatile returns increases the chance that an investor could end up with a positive return.

Assuming that participants should always regard the high-volatility asset as more risky (which may not hold e.g. in trend $NEGATIVESTABLE$ ), we can distinguish between ‘correct’ and ‘incorrect’ choices. Along this line we compare the proportion of the two between conditions $VOLATILITY$ and $BOTH$ —where the scale is either the same for both assets or adapted to the respective asset’s volatility. On average, we find that the percentage of ‘incorrect’ choices, in which either the two assets are regarded as being equally risky or the low-volatility asset is seen as riskier, is significantly lower in Condition $VOLATILITY$ (13%) than in Condition $BOTH$ (29%, $p<0.01$ ).Footnote ¹⁸ Hence, adapting the scale to the returns’ magnitude leads to significantly more mistakes when assessing the riskiness of two assets with differing levels of volatility.

4.2 Perceived profitability in pairwise comparisons

We now turn to the analysis of perceived profitability in pairwise comparisons. The respective proportions for this variable are depicted in the second bar of each group of bars in Fig. 7 (‘profit.’).

Result 6 Scaling can distort people’s perception about an asset’s profitability in pairwise comparisons of assets with the same volatility. For trends $POSITIVESTABLE$ and $INCREASING$ , assets shown on a $NARROW$ scale are regarded as more profitable; for trends $NEGATIVESTABLE$ and $DECREASING$ , the opposite holds.

Support In the top row of panels in Fig. 7, showing results for Condition $SAME$ , between 28% and 65% of subjects state a difference in perceived profitability, even though the two assets are essentially identical. The patterns observed, both with $RETURN$ charts (left panels) and $PRICE$ charts (right panels) are almost identical to the ones from perceived riskiness (first bar, ‘risk’, in each group of bars).

When volatility and expected returns are the same but the charts are shown with different scaling (Condition $SCALE$ ; see second row of panels in Fig. 7), we find that between 49 and 72% of subjects (correctly) see no difference in profitability. However, up to 51% do see a difference. For the $POSITIVESTABLE$ and $INCREASING$ trends (first two groups of bars of each panel) the results are again similar to those for perceived riskiness—the asset shown with narrow scaling is perceived as the more profitable one as the (mostly positive) bars are displayed larger here. For the $NEGATIVESTABLE$ and $DECREASING$ trends, however, we find a marked difference: those 28% to 46% of subjects who do perceive a difference in profitability largely identify the asset displayed with wide scaling as more profitable—the mostly negative returns are shown with smaller bars and subjects are misled to think these are thus more profitable. Subjects fall into this ‘trap’ in between 18% and 33% of all decisions.

With regard to the change in scales between the two conditions, we observe similarly high numbers of ‘correct’ profitability assessments (in the sense of regarding the two essentially identical assets as equally profitable) for all trends except for $INCREASING$ , for which we observe fewer mistakes in Condition $SCALE$ . Overall, in 55% ( $SAME$ ) and 60% ( $SCALE$ ) of decisions, respectively, subjects assess the two as equally profitable.

Result 7 Scaling can distort people’s perception about an asset’s profitability in pairwise comparisons of assets with different volatilities. With the same scale, more volatile assets of trends pos. stable and $INCREASING$ are regarded as more profitable; for trends neg. stable and $DECREASING$ , the opposite holds. With different scales, a large share perceives the low-volatility asset as more profitable.

Support The third row of panels in Fig. 7 presents Condition $VOLATILITY$ , in which for $PRICE$ charts there are more extreme prices for $HIGH$ -volatility assets—that is, the $HIGH$ -volatility asset yields higher prices with trends $POSITIVESTABLE$ and $INCREASING$ and lower prices with trends $NEGATIVESTABLE$ and $DECREASING$ (compared to the respective $LOW$ -volatility assets). While almost 100% of subjects perceive the asset with the higher volatility as the riskier one with a $POSITIVESTABLE$ trend, we find 21% of subjects to assess the less risky asset as the more profitable one in this trend with $RETURN$ charts. It seems that for profitability assessments subjects also take a lower volatility into account. Most notably, however, we observe the same pattern as above: for $POSITIVESTABLE$ and $INCREASING$ trends (first two groups of bars of each panel), most subjects perceive the more volatile asset as the more profitable one (as the returns bars are mostly positive, respectively the price mostly increases), while for the $NEGATIVESTABLE$ and $DECREASING$ trends (last two groups of bars of each panel), the opposite holds and the mostly negative returns/falling prices lead subjects to select the low-volatility asset as the more profitable one. For the latter two price trends the ‘indifferent’ choices are also markedly higher than for the positive price trends ( $p<0.01$ for $RETURN$ charts, $p<0.05$ for $PRICE$ charts)—probably because subjects see both assets markedly going down and consider this a decision ‘between a rock and a hard place’, i.e. a choice between two equally bad alternatives.

Finally, for Condition $BOTH$ we find shares of 29% to 66% of decisions in which subjects consider the asset with the lower volatility to be the more profitable one in the $NEGATIVESTABLE$ and $DECREASING$ trends. In addition, also in the two other trends (first two groups of bars) the share of subjects considering the low-volatility asset as the more profitable one is substantial, especially when $RETURN$ charts are displayed. These shares of up to 38% are markedly higher than the respective shares for perceived riskiness ( $p<0.01$ ).

Comparing the proportion of ‘correct’ assessments in the sense of regarding the asset with a higher average return as more profitable between conditions $VOLATILITY$ and $BOTH$ we can again analyze the effect of adapting the scale with respect to the magnitude of returns. While on average the frequency of a ‘correct’ choice is higher (56%) with same scales (Condition $VOLATILITY$ ) compared to adapted scales (52%; Condition $BOTH$ ), this difference is not statistically significant.

4.3 Investment preferences in pairwise comparisons

In Task II we ask as a third question which of the two displayed assets subjects would rather invest in and incentivize this question by paying subjects one randomly determined return from the chosen asset. This allows us to examine the behavioral consequences of the scale effects reported above. The third bar in each set of bars in Fig. 7 (‘inv.’) shows the respective shares of investments in one of the two displayed assets.

In Condition $SAME$ a considerable fraction of subjects sees the two displayed assets as bearing different risks and profitabilities. A still higher share of between 33 and 86% of subjects decide to invest in either of the two. The share of ‘indifferent’ choices is smaller for investment preferences than for riskiness and profitability. This holds for each trend and both presentation formats. As the investment propensity is a function of both risk perception and return expectations, perceived differences in either of the two factors can lead to a difference in the investment propensity. Thus, the share of indifferent subjects should logically be smaller for investment propensity than it is for any of the two other variables. Additionally, the increase in decisiveness could also be attributable to the monetary incentives associated with this particular question.

For Condition $SCALE$ , we find a considerable effect of the axis scale regarding investment decisions. Here, choices tend to be very similar to profitability assessments: as two identical assets are compared, assets presented on a $NARROW$ scale are more frequently preferred for trends $POSITIVESTABLE$ and $INCREASING$ , whereas for trends $NEGATIVESTABLE$ and $DECREASING$ , the opposite holds (with the exception of $INCREASING$ in $PRICE$ charts). Comparing conditions $SAME$ and $SCALE$ vertically reveals how the scale affects subjects’ behavior: we find on average a much less pronounced indifference between the two displayed assets in $SAME$ (44% vs. 57%, $p<0.01$ ).

In the pairwise comparisons of conditions $VOLATILITY$ and $BOTH$ , we observe a number of diverging preferences—i.e., especially when return charts are displayed a large fraction chooses to invest in the $HIGH$ -volatility asset and a similarly large fraction chooses to invest in the $LOW$ -volatility asset. The variation of the scale between these two conditions (same or different) does not result in a systematic difference in investment preferences.

Naturally, we are interested in how perceived riskiness and perceived profitability relate to people’s investment decisions. Comparing the shares of answers regarding investment preferences with the corresponding values concerning perceived riskiness (first bar, ‘risk’) and profitability (second bar, ‘profit.’) already hints at a meaningful relationship between these variables with the tendency of more investments in assets which are perceived as less risky and more profitable.

For a more thorough analysis we estimate the probability with which a subject invests in either the $NARROW$ -scaled or in the $HIGH$ -volatility asset, respectively, depending on which asset she perceives as more risky and as more profitable, by running probit regressions.Footnote ¹⁹ The resulting probabilities are plotted in Fig. 8.

Fig. 8

Predicted probabilities of investing in the $HIGH$ -volatility or $NARROW$ -scaled asset. This figure shows the predicted probabilities and 95%-confidence intervals of investing in the $HIGH$ -volatility ( $NARROW$ -scaled) asset depending on which asset is perceived as more risky (top) or as more profitable (bottom). Probabilities are estimated from a probit model with a dummy variable indicating whether the subject would invest in the $HIGH$ -volatility ( $NARROW$ -scaled) asset as the dependent variable and her choice regarding riskiness and profitability as independent variables. The numbers of observations for each estimation lie between 171 and 222 for different presentation formats and trends

Result 8 Regarding one of two assets as more profitable and less risky leads to a higher probability of investing in this asset. Of the two factors profitability tends to be more important.

Support Regarding the effect of perceived riskiness (top panel of Fig. 8), we observe that in cases when a subject perceives the $LOW$ volatility or the $WIDE$ -scaled asset as more risky, the probability that she invests in the $HIGH$ volatility or $NARROW$ -scaled asset is between 68% and almost 100% across trends with return charts and even higher for price charts. Conversely, only around 25% tend to invest in this asset if it is perceived as riskier in trends $NEGATIVESTABLE$ and $DECREASING$ , with a significantly higher number for trends $POSITIVESTABLE$ and in-creasing.

For price charts the probability of investing in the asset with higher perceived risk is 61 and 54%, respectively, with these trends—indicating that perceived risk is not necessarily the main determinant of investment behavior in the domain with mostly positive returns. Investing in the higher-volatility asset need not be a ‘wrong’ choice—especially in the case of a $NEGATIVESTABLE$ trend having more volatile returns increases the chance that an investor could end up with a positive return. Such choices are thus in line with Prospect Theory (Kahneman and Tversky Reference Kahneman and Tversky1979) which postulates risk-seeking behavior in the loss domain, where returns of assets with a $NEGATIVESTABLE$ trend mostly are (assuming zero return as subjects’ reference point). Hence, subjects who prefer the high-volatility asset over the low-volatility one in $NEGATIVESTABLE$ (and with lower shares also in $INCREASING$ and $DECREASING$ trends) should not be judged ‘irrational’ or ‘incorrect’, but can merely be risk-seeking in the loss domain.

Analyzing probabilities to invest depending on perceived profitability (bottom panel) we observe very similar estimates across all trends. If the $HIGH$ volatility ( $NARROW$ -scaled) asset is perceived as more profitable, the probability of a subject investing in this asset is also very high (between 74 and 86%), and vice versa. As we observe comparable dynamics for all trends we conclude that perceived profitability is more important than perceived riskiness in these decisions. Subjects tend to invest in the asset which they regard as more profitable, even if they think it bears higher risk.